Modal vibration parameters such as frequency, damping ratio and mode shape have long been considered useful for identifying damage in structures. In this paper a generalized approach is presented that allows for damage to be localized and quantified using regression and response surface modeling of modal frequency. Regression models or response surface models are developed to characterize how modal frequencies of structures are affected by variations in parameters such as defect depth, width and location. Design of experiments (DOE) techniques are used in conjunction with experimental modal frequency measurements to solve for defect parameters of test specimens in the field for condition monitoring. Determining defect parameters can be done by inverting and explicitly solving regression model equations, employing software-driven numeric optimization or through a graphical approach that overlays contour lines of multiple response surface models. Either of these methods can be automated. This approach is explored and validated with finite element and theoretical beam models along with a series of physical experiments on cantilevered aluminum rods. The method performs well for detecting simple and distinct defects. Implementation complexity increases when detecting multiple or more variable, less-easily quantifiable defects. In its general form, the method shows promise for damage detection when a specific type of consistent defect is known to occur or for applications such as quality control on production lines and monitoring of deposit buildup in pipes.
Optimal design of experiments for non‐linear response surface models